Table 1.

List of mathematical notations.

Sets
I	Set of demand points
J	Set of priority groups
N	The target total number of doses to be completed for the entire course of vaccination of a type of vaccine
K	Set of costs
Parameters
i	Demand points, i ∈I
j	Priority groups, j ∈J
n	The dose of vaccine that has been administered to the target population (0 ≤ n<N)
k	Types of costs for vaccine distribution
P	Total population of all regions
pij	The number of the target population in group j in demand point i
pijn	The number of the target population who had received n dose(s) of the vaccine in group j in demand point i
μijn	The proportion of the target population with n dose(s) who will not receive the vaccine in group j in demand point i
αn	The expected proportion of people who have been vaccinated with n dose(s)
θj	Minimum vaccination coverage in group j
Q	The total amount of vaccines in the supply center
Qi	Capacity of vaccine storage in warehouse of demand point i
TCik	Type k cost of a single dose of vaccine in demand point i
BG	Budget
Variables
yijn	Integer, the number of individuals vaccinated in group j vaccinated with n dose(s) in area i
xijn	Integer, the number of vaccines allocated in group j in the area i vaccinated with n dose(s)